Flying to Kampala with a tailwind a plane averaged 158 km/h. On the return trip the plane only
averaged 112 km/h while flying back into the same wind. Find the speed of the wind and the speed of
the plane in still air.
TIA
To find the speed of the wind and the speed of the plane in still air, we can set up a system of equations using the given information.
Let's denote the speed of the plane in still air as "p" and the speed of the wind as "w".
On the trip to Kampala with a tailwind, the plane's speed is increased by the speed of the wind. So the effective speed is p + w. We are given this speed as 158 km/h.
On the return trip against the same wind, the plane's speed is decreased by the speed of the wind. So the effective speed is p - w. We are given this speed as 112 km/h.
We can now set up the equations:
p + w = 158 ----(1)
p - w = 112 ----(2)
To solve this system of equations, we can use the method of addition or elimination.
Add equations (1) and (2) to eliminate "w":
(p + w) + (p - w) = 158 + 112
2p = 270
p = 270/2
p = 135
Now, substitute the value of p into equation (1) or (2) to find the value of "w":
p + w = 158
135 + w = 158
w = 158 - 135
w = 23
Therefore, the speed of the wind is 23 km/h and the speed of the plane in still air is 135 km/h.
speed out = 158 = v+w
speed back = 112 = v-w
add the two equations
2 v = 270
v = 135
w = 158 - 135 = 23